Department №50 Physics of multi-particle systems

The main research areas of the Dept #50 Physics of multi-particle systems:

1. Investigation of the nucleus-nucleus interaction processes involving the light nuclei at intermediate energies.

   The processes of elastic and inelastic scattering, and a variety of quasi-elastic nuclear reactions of light nuclei at intermediate energies by light nuclei are linked by a common peculiarity that they occur at the distances correspond to the deep mutual penetration of colliding nuclei. Because of the mentioned, these reactions are the unique source of information about the nucleus-nucleus interaction at the short distances and about the structure of scattered nuclei.

   To analyze the experimental data on the scattering and quasi-elastic reactions of the light nuclei at intermediate energy on the nuclei, the different S-matrix models are traditionally used. The optical model is used to describe the elastic scattering, the coupled-channel and distorted waves methods are also used in case of the inelastic scattering and direct nuclear reactions. The specified above experimental results attract researcher's attention because they contain the manifestations of the various refractive phenomena determined by the properties of the nucleus-nucleus interactions on nuclei at the short distances.

   For the analysis of experimental data the use of the simple S-matrix models, which scattering phase responsible for the absorption and nuclear refraction are determined by the Fermi or Gaussian functions, and as well as the optical model potentials according to the mentioned S-matrix model representations, turned out successfully and helped to interpret the observed scattering pattern as a manifestation of nuclear rainbow in the presence of strong absorption. However, usually such models can not correctly describe all the details of the complex behavior of the studied differential cross sections of the nucleus-nucleus scattering.

   Quality of agreement between calculated and observed cross sections can be improved if we modify the phase describing the nuclear absorption and refraction through attaching the additional surface components of different shapes. These modifications result in a non-monotonic dependence of the specified scattering phases on the orbital moment, which occurs mostly in the narrow regions of moments. However, the "rainbow" interpretation of the behavior of the studied cross-sections is still urgent.

   The subsequent significant quality improvement of the description of experimental data is possible, if we choose the S-matrix in a more flexible form when responsible for the absorption and refraction phases are non-monotonic functions in all possible values of the orbital moment. The scattering matrices have the following behavior when to the commonly used model representations, that are smooth monotonic functions of orbital moment, add a few components with polar character or are represented as a suitable decomposition on a set of basic functions, such as spline functions. The indicated characteristic attribute of non-monotonic bihavior is also inherent to the scattering matrices calculated using the optical potentials, which have the additional components localized on the absorbtion interval (nuclear refraction), which in their turn have a form in terms of total volume derivatives, or a more complex form fitted with the spline functions or the Fourier-Bessel series. Despite the fact that according to the specified approaches, the excellent agreement between calculated and obtained differential cross-sections of nucleus-nucleus scattering at the intermediate energies is achieved, and estimated results show that the "rainbow" interpretation of data in these cases is not applicable. Thereby, this raises a question about the physical meaning of the non-monotonic structures founded in the S-matrix.

   It should be noted that all the discussed approaches are somehow model-dependent because they are based on the selection of scattering phases in a kind of the clearly parameterized analytical functions. So that, there is no possibility to take into account a huge variety of all possible forms of scattering matrix (nucleus-nucleus potential). Therefore the analysis of experimental data performed applying a limited number of possible forms of S-matrix (potential) may lead in certain cases to wrong physical interpretation of analyzed data.

   In this regard, the development of procedures for obtaining the scattering matrix and the nucleus-nucleus potential directly from the experimental data without any a priori physically based model assumptions about their form is very important and urgent. Thus there is a necessity to study the properties of forms of the mentioned characteristics of nucleus-nucleus interactions and, if required, to provide an appropriate degree of their smoothness and absence of any form of distortions due to the automatic control of derivatives of scattering phases (real and imaginary parts of the nucleus-nucleus potential). Implementation of this approach is possible through using the evolutionary algorithm. This algorithm allows as a result of the gradual and smooth transformation of the initial population of scattering matrices, which does not lead to any satisfactory agreement with experimental data, to obtain the final population of scattering matrices that provides a valid description of the analysed data. It is important that the final result does not depend on the composition of the initial population, as well as on the smooth modification method of the scattering matrix during mutation, and the results of data processing both quantitatively and qualitatively exceed the results of the others, more successful approaches.

   We obtained the next results in this area:

   The universal method for getting the certain important physical characteristics (eg, the interaction potentials for ions, molecules, the scattering matrices for nuclei, the order parameter, which minimizes the free energy functional, and other variables, which for the various reasons can not be measured experimentally and for their estimation traditionally a variety of model approaches are used) is proposed directly from the experimental data without involving any a priori physically based model assumptions about their behaviour. This method is based on the application of an evolutionary algorithm that provides the output of the final population of equilibrium distributions of the studied characteristics throung their smooth deformation.

   A number of problems, associated to various aspects of the interaction of light nuclei with nuclei in a wide energy range of incident particles, are formulated and solved. In particular, the theoretical approach, based on the S-matrix formalism, was developed to describe on the single basis of refractive effects of the elastic and inelastic scattering of light nuclei by nuclei. Based on the mentioned approach, the experimentally obtained differential cross sections of scattering of light nuclei with energies E ≥ 20 - 25 MeV /nucleon by the spherical nuclei and deformed nuclei sd-shell are described in a wide interval of scattering angles, it also helped to select the additives to the differential cross-sections defined by the nuclear refraction and strong nuclear absorption [9 - 16].

2. Investigation on the deformation dynamics of the surface of light nuclei

   Spectroscopic data for light nuclei with 2s1d shell are a source of important information about the deformation of the nucleus surface shape in both the ground and excited states. Unfortunately, the parameters of the nucleus deformation are impossible to get directly from the experimental data. Therefore, the different model representations of the shape of the atomic nucleus and its dynamics during the transitions between the stationary states are traditionally used to obtain such information.

   For the analysis of the experimentally measured spectroscopic data of light nuclei, one of the most popular approaches is the Nilsson model (with various refinements, additions and modifications), which applies the axially- symmetric oscillator one-particle shell potential, the potential of spin-orbit interaction and a special potential proportional to the square of the orbital moment of each individual nucleon. Besides of the deformation magnitudes, among the parameters of this model are the weight operators of the spin-orbit interaction and the squared value of the orbital moment. It has been proven that neither the standard set of values of these parameters proposed by Nilsson, nor their fitting do not allow to reproduce simultaneously the experimentally obtained values of energies as well as the quantum characteristics of the states. The calculations have shown that a good agreement of calculated with measured data can be achieved if substantially reduce the contribution of the radial dependence of the shape of the deformed nucleous surface in the Nilsson hamiltonian. Scilicet, the real form of the potential of the axially deformed nucleus is much more complex than assumed in the Nilsson model.

   As for an example problem, we demonstrated for spectrum of the one-dimensional quantum oscillator that for the known energy spectrum of its Hamiltonian, our algorithm reproduces very well the shape of oscillator potential. Therefore, for the classical inverse scattering problem we obtain the simple numerical solution within our non-model approach [17 - 24].

3. Research on evolutionary algorithms and their application for problems in nuclear physics and energetics

   1. Intelligent controller of technological processes.

   The primary goal of building the adaptive control systems is to minimize human involvement in configuring the controls in order to achieve the optimal control of some object. Nowadays, the proportional-integral-derivative controllers (PID) are mainly used in the control systems. However, the common PID controller does not satisfy the requirements of novel developing technologies of the following reasons. Firstly, in order to control precisely a process it is necessary to change operatively the controller settings, that is usually accompanied with the changes of load on the facility, with a variation in composition and quality of materials, aging equipment (i.e. growth of scum & buildup in heat exchangers, spoilage of furnace lining etc.), the influence of external temperature and humidity with changing of the seasons, the reconstruction or replacement of the equipment that is a part of a complex process etc. Second, the precise adjustment of the process without any overshoot affects decreasing of energy consumption. Therefore, a controller should independently determine the type of object, select and control automatically the adjustment parameters in processes as well as spend minimum of time to change the operating regime.

   So that, the question of application of the highly efficient control techniques using the principles of adaptive control (ie, control that provides the optimal adjustment at a priori unknown uncertain mathematical model of unexpectedly changeable object) becomes very important.

   There are the recent results on this topic:

   The method of the effective computer generation of syntactically correct algebraic expressions of arbitrary complexity was developed using the evolutionary algorithm (the symbolic regression). We studied methodology of inserting arbitrary constant values into the algebraic expressions of arbitrary complexity and their determination using the evolutionary algorithm. The special software, based on the evolutionary algorithm, was developed to solve numerically the differential equations of arbitrary complexity. In the dept#50, the computer code was written to demonstrate the evolutionary modeling of the optimal controller based upon an example of the common PID controller and of the easy control object, which is described by the second order differential equations. The proposed approach involves a dynamic automatic selection of the most adequate model of the control object and the most optimal control model.

   2. Analysis of component composition of radioactive samples.

   One of the most important problems in modern nuclear energetics is the safe storage and utilization of radioactive waste. An integral part of solving this problem is to control dynamically the state of radioactive waste in storage and the ability to predict changes in the composition and state of waste over time.

   The fundamental possibility to control dynamically the component composition in radioactive samples is caused by the fact that the dependence of the complete activity of a radioactive sample on time is given by the law of radioactive decay. We have an opportunity to determine the number of radioactive nuclei of some sort at some time and their half-decay periods through dynamic controlling of the total activity of sample and optimizing the parameters of the decay law.

   We developed and implemented a new evolutionary algorithm for determination of the quantity of radioactive nuclei of any sort and their half-lives, that are necessary to obtain some information about the component composition, for example, of radioactive waste. The software, developed using the evolutionary computer technologies, allows at any time moment to analyze and predict changes through time, as for instance, we can estimate the changes in the containers with radioactive waste.

   The practical importance of our results is that we can implement them in the programmable detecting, controlling and regulating devices for the technological processes and NPP safety systems. We can also use the evolutionary algorithms to solve other problems associated with nuclear power, such as the optimization of work schedule, maintenance and decommissioning of nuclear fuel, repair work optimization on the nuclear reactors and enhancement of methods for developing of the new construction materials for NPP, as well as solving a great variety of environmental problems. Finally, developing of new computer models and algorithms will help to extend the operational life span of nuclear power plants.